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In the service period, some engineering structures may have cracks or other nonlinear damages. The nonlinear damages are the major influence to the safety of engineering structures, which should be detected as early as possible. Currently, the effective nonlinear damage detection method is still lacking. Therefore, a penalty conversion index based on generalized autoregressive conditional heteroskedasticity (GARCH) model is presented to identify the nonlinear damage. First, an exact expression of GARCH model is described, the bilinear stiffness characteristic of nonlinear damage is given, and acceleration responses are used to establish the GARCH model. Then, through the GARCH model analysis of nonlinear damages responses, it can be found that the variance of conditional variance are sensitive to the nonlinear damage information of acceleration responses, so a basic conversion index based on the variance of conditional variance is proposed. Finally, a penalty conversion index based on GARCH model is presented, which can reduce the interference induced by the adjacent unrelated factors. Numerical and experimental examples show that the identification results of the proposed penalty conversion index based on GARCH model are superior to those of the basic conversion index and the cepstral metric (CM) index.

It is difficult for the traditional methods to identify uncertain damage problems caused by noise. Therefore, a gray cloud rule generator algorithm based on cloud model and modal strain energy is presented to solve the problems. Cloud model can simulate both randomness and fuzziness with fixed parameters. Therefore, it is applicable for the uncertain damage problems. First, modal strain energy and modal strain energy dissipation ratio index are introduced. Then, numerical characteristics of a cloud model are described and some cloud generators are analyzed. Finally, a gray cloud rule is proposed and the gray cloud rule generator algorithm based on the gray cloud rule generator and modal strain energy is developed. The interference of uncertain noise is reduced through a large number of cloud droplets. A two-dimensional truss structure model has been used to verify the effectiveness of the algorithm. The results indicate that the proposed gray cloud rule generator algorithm is applicable to identify the uncertain damage caused by noise, and the identification results of the proposed method are relatively better than those of modal strain energy dissipation ratio index.